Data Sufficiency Flashcards

Is n an even integer? (1) n/2 is an integer. (2) 3n is even.

Answer: Each statement alone is sufficient.

Statement (1): n/2 is integer means n is divisible by 2, so n is even. Statement (2): 3n even means n must be even (since 3 is odd). Each alone is sufficient.

What is the perimeter of triangle ABC? (1) AB = BC = 8. (2) The triangle is equilateral.

Answer: Both statements together are sufficient, but neither alone.

Statement (1) gives two sides as 8 but not the third; Statement (2) says all sides equal but not their length; together: equilateral with AB=8 means all sides=8, perimeter=24.

A store's profit increased by what percent last year? (1) Profit increased by $50,000. (2) Last year's profit was $250,000.

Answer: Both statements together are sufficient, but neither alone.

Percent increase = $50K / $250K × 100 = 20%; both statements are needed to calculate the percentage.

Is xy > x? (1) y > 1. (2) x > 0.

Answer: Both statements together are sufficient, but neither alone.

If y > 1 and x > 0, then xy > x (multiplying both sides of y>1 by positive x). Neither alone is sufficient.

What is the value of a² − b²? (1) a + b = 10. (2) a − b = 4.

Answer: Both statements together are sufficient, but neither alone.

a² − b² = (a+b)(a−b) = 10 × 4 = 40; both statements together are sufficient using the difference of squares factoring.

A company has how many employees? (1) The ratio of managers to non-managers is 1:9. (2) There are 30 managers.

Answer: Both statements together are sufficient, but neither alone.

Statement (1) gives ratio; Statement (2) gives the number of managers; together: 30 managers + 270 non-managers = 300 total.